Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase

In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.

In this paper, the weak(1, 1) boundedness of oscillatory singular integral with variable phase P(x)γ(y) for any x, y ∈ R,■is studied, where P is a real monic polynomial on R.